Check force on energy

It is common practise to use the potential energy as a collective energy. Some MD codes thus pass the potential energy to PLUMED and PLUMED can then apply forces on this collective variable. We test that any forces that PLUMED applies on the potential energy are correctly passed back to the MD code by doing the following test. We first run a short simulation at $T$ K with a timestep of $\tau$ ps. During the course of this simulation we monitor the potential energy using the following PLUMED input:

Click on the labels of the actions for more information on what each action computes
tested on2.10
tested onmaster
e: ENERGYCalculate the total potential energy of the simulation box. More details
v: VOLUMECalculate the volume the simulation box. More details
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=e,v FILEthe name of the file on which to output these quantities=energy1

We then run a second simulation (starting from identical conditions) at a temperature of $T\alpha$ and with a timestep of $\tau/\sqrt(\alpha)$. The thermostat and barostat relaxation times are similarly divided by $\sqrt(\alpha)$. In the tests that are run on this website we set $\sqrt(\alpha)=1.1$. The PLUMED file above is used when this test is run but a different time series of energy values is recorded as the MD parameters in this second simulation are different.

If PLUMED is working correctly we should be able to recapture the time series of energy values for the first simulation by running an MD simulation with the modified parameters that were used in the second simulation and the following PLUMED input file:

Click on the labels of the actions for more information on what each action computes
tested on2.10
tested onmaster
e: ENERGYCalculate the total potential energy of the simulation box. More details
v: VOLUMECalculate the volume the simulation box. More details
# slope is such that 
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=e FILEthe name of the file on which to output these quantities=energy2
# slope should be (alpha-1)=0.21
RESTRAINTAdds harmonic and/or linear restraints on one or more variables. More details ATthe position of the restraint=0.0 ARGthe values the harmonic restraint acts upon=e SLOPE specifies that the restraint is linear and what the values of the force constants on each of the variables are=0.21

In other words, when forces are passed correctly the time series for the energies and volumes from the first and third of these calculations should be identical.

To determine if PLUMED passes this test we calculate the difference between the time series that were observed in the first and third simulations described above. We then divide this by the difference between the first and second time series.

An NPT version of this calculation is performed as well as an NVT calculation if the virial is passed to PLUMED.

Trajectories

  1. Input and output files for the unpeturbed calculation are available in this zip archive

  2. Input and output files for the peturbed calculation are available in this zip archive

  3. Input and output files for the peturbed calculation in which a PLUMED restraint is used to undo the effect of the changed MD parameters are available in this zip archive

Results

Original With PLUMED Effect of peturbation % Difference
-18174.8223 11.6346 -18174.8223 11.6346 0.0000 0.0000 0.0000 0.0000
-18171.8203 11.6346 -18193.2891 11.6346 6.8730 0.0000 312.3615 0.0000
-18194.3809 11.6475 -18231.9336 11.6321 22.4121 0.0054 167.5556 284.9140
-18167.2266 11.6475 -18280.5840 11.6321 18.4043 0.0054 615.9291 284.9140
-18154.7012 11.6475 -18314.7422 11.6321 21.1387 0.0054 757.1006 284.9140
-18137.2773 11.6475 -18332.2324 11.6321 22.1855 0.0054 878.7481 284.9140
-18120.5566 11.6475 -18334.4102 11.6321 23.5547 0.0054 907.9021 284.9140
-18110.3613 11.6475 -18328.1992 11.6321 26.8281 0.0054 811.9758 284.9140
-18109.8691 11.6475 -18321.5801 11.6321 31.9863 0.0054 661.8794 284.9140
-18117.8613 11.6475 -18319.6328 11.6321 37.0938 0.0054 543.9501 284.9140
-18129.6270 11.6475 -18322.9863 11.6321 39.6074 0.0054 488.1898 284.9140
-18139.7188 11.6475 -18329.3066 11.6321 38.2051 0.0054 496.2374 284.9140
-18145.7422 11.6475 -18336.4648 11.6321 34.7168 0.0054 549.3671 284.9140
-18150.4473 11.6475 -18345.3516 11.6321 33.7754 0.0054 577.0601 284.9140
-18159.7363 11.6475 -18358.9492 11.6321 39.5723 0.0054 503.4154 284.9140
-18177.3867 11.6475 -18378.7109 11.6321 51.3574 0.0054 392.0061 284.9140
-18200.4512 11.6475 -18400.8438 11.6321 62.0566 0.0054 322.9188 284.9140
-18220.1230 11.6475 -18417.2480 11.6321 62.5273 0.0054 315.2621 284.9140
-18227.3770 11.6475 -18420.6094 11.6321 48.5371 0.0054 398.1128 284.9140
-18218.8027 11.6475 -18409.3438 11.6321 24.2227 0.0054 786.6231 284.9140

The table below includes some of the results from the calculation. The columns contain:

  1. Time series for the energy and volume that were obtained from the simulation at $T$ K, $x_{md}$.
  2. Time series for the energy and volume that were obtained from the simulation at $\alpha T$ K and in which PLUMED applied a restraint on the energy, $x_{pl}$.
  3. The absolute value of the difference between the time series of energies and volumes that were obtained from the simulations running at $T$ K and $\alpha T$ K, $\vert x_{md}’-x_{md} \vert$. No PLUMED restraints were applied in either of these simulations.
  4. The values of $100\frac{\vert x_{md} - x_{pl}\vert }{ \vert x_{md}’-x_{md} \vert}$.

If the PLUMED interface is working correctly the first two sets of numbers should be identical and the final column should be filled with zeros.

Graphical representation (beta)

A visualization of the table above:
engvir_master